Maximal prime gaps are gaps which are larger than all gaps between smaller primes. Gaps
with + before the merit also have larger merit than all gaps between smaller
primes. merit = size / log(gap start).

Maximal gaps

No

Size

Gap start

Merit

Discoverer

Year

1

1

P1 = 2

+1.44

2

2

P1 = 3

+1.82

3

4

P1 = 7

+2.06

4

6

P2 = 23

1.91

5

8

P2 = 89

1.78

6

14

P3 = 113

+2.96

7

18

P3 = 523

2.88

8

20

P3 = 887

2.95

9

22

P4 = 1129

+3.13

10

34

P4 = 1327

+4.73

11

36

P4 = 9551

3.93

12

44

P5 = 15683

4.55

13

52

P5 = 19609

+5.26

14

72

P5 = 31397

+6.95

15

86

P6 = 155921

+7.19

16

96

P6 = 360653

+7.50

17

112

P6 = 370261

+8.74

18

114

P6 = 492113

8.70

19

118

P7 = 1349533

8.36

20

132

P7 = 1357201

+9.35

21

148

P7 = 2010733

+10.20

22

154

P7 = 4652353

10.03

23

180

P8 = 17051707

+10.81

Derrick Henry Lehmer

1957

24

210

P8 = 20831323

+12.46

Derrick Henry Lehmer

1957

25

220

P8 = 47326693

12.45

Kenneth I. Appel & J. Barkley Rosser

1961

26

222

P9 = 122164747

11.92

L. J. Lander & Thomas R. Parkin

1967

27

234

P9 = 189695659

12.28

L. J. Lander & Thomas R. Parkin

1967

28

248

P9 = 191912783

+13.00

L. J. Lander & Thomas R. Parkin

1967

29

250

P9 = 387096133

12.64

L. J. Lander & Thomas R. Parkin

1967

30

282

P9 = 436273009

+14.18

L. J. Lander & Thomas R. Parkin

1967

31

288

P10 = 1294268491

13.73

L. J. Lander & Thomas R. Parkin

1967

32

292

P10 = 1453168141

13.84

L. J. Lander & Thomas R. Parkin

1967

33

320

P10 = 2300942549

+14.84

L. J. Lander & Thomas R. Parkin

1967

34

336

P10 = 3842610773

+15.22

L. J. Lander & Thomas R. Parkin

1967

35

354

P10 = 4302407359

+15.96

L. J. Lander & Thomas R. Parkin

1967

36

382

P11 = 10726904659

+16.54

L. J. Lander & Thomas R. Parkin

1967

37

384

P11 = 20678048297

16.17

Richard P. Brent

1973

38

394

P11 = 22367084959

16.53

Richard P. Brent

1973

39

456

P11 = 25056082087

+19.04

Richard P. Brent

1973

40

464

P11 = 42652618343

18.96

Richard P. Brent

1973

41

468

P12 = 127976334671

18.30

Richard P. Brent

1973

42

474

P12 = 182226896239

18.28

Richard P. Brent

1973

43

486

P12 = 241160624143

18.54

Richard P. Brent

1973

44

490

P12 = 297501075799

18.55

Richard P. Brent

1973

45

500

P12 = 303371455241

18.91

Richard P. Brent

1973

46

514

P12 = 304599508537

+19.44

Richard P. Brent

1973

47

516

P12 = 416608695821

19.29

Richard P. Brent

1973

48

532

P12 = 461690510011

+19.81

Richard P. Brent

1973

49

534

P12 = 614487453523

19.67

Richard P. Brent

1973

50

540

P12 = 738832927927

19.76

Richard P. Brent

1973

51

582

P13 = 1346294310749

+20.84

Richard P. Brent

1973

52

588

P13 = 1408695493609

+21.02

Richard P. Brent

1973

53

602

P13 = 1968188556461

+21.27

Richard P. Brent

1973

54

652

P13 = 2614941710599

+22.80

Richard P. Brent

1973

55

674

P13 = 7177162611713

22.77

Jeff Young & Aaron Potler

1989

56

716

P14 = 13829048559701

+23.66

Jeff Young & Aaron Potler

1989

57

766

P14 = 19581334192423

+25.03

Jeff Young & Aaron Potler

1989

58

778

P14 = 42842283925351

24.79

Jeff Young & Aaron Potler

1989

59

804

P14 = 90874329411493

25.02

Jeff Young & Aaron Potler

1991

60

806

P15 = 171231342420521

24.59

Thomas R. Nicely

1995

61

906

P15 = 218209405436543

+27.44

Thomas R. Nicely

1996

62

916

P16 = 1189459969825483

26.39

Thomas R. Nicely

1998

63

924

P16 = 1686994940955803

26.35

Bertil Nyman

1999

64

1132

P16 = 1693182318746371

+32.28

Bertil Nyman

1999

65

1184

P17 = 43841547845541059

30.90

Bertil Nyman

2002

66

1198

P17 = 55350776431903243

31.07

Tomás Oliveira e Silva

2002

67

1220

P17 = 80873624627234849

31.34

Tomás Oliveira e Silva

2003

68

1224

P18 = 203986478517455989

30.71

Tomás Oliveira e Silva

2005

69

1248

P18 = 218034721194214273

31.26

Tomás Oliveira e Silva

2005

70

1272

P18 =
305405826521087869

31.59

Tomás Oliveira e Silva

2006

71

1328

P18 =
352521223451364323

+32.87

Tomás Oliveira e Silva

2006

72

1356

P18 = 401429925999153707

+33.45

Donald E. Knuth

2006

73

1370

P18 = 418032645936712127

+33.77

Donald E. Knuth

2006

74

1442

P18 = 804212830686677669

+34.98

Siegfried Herzog & Tomás Oliveira e Silva

2005

75

1476

P19 =
1425172824437699411

+35.31

Tomás Oliveira e Silva

2009

The search is exhaustive to 4×1018 as of 30 December 2015.
The Top-20 merits
include a few known prime gaps with larger merit than any of the above. They are between far larger primes and
extremely unlikely to be maximal gaps. As of 25 August 2016, the largest known
merit is: